A comparison of different procedures for principal component analysis in the presence of outliers

Abstract

Principal component analysis (PCA) is a popular technique that is useful for dimensionality reduction but it is affected by the presence of outliers. The outlier sensitivity of classical PCA (CPCA) has caused the development of new approaches. Effects of using estimates obtained by expectation-maximization -EM and multiple imputation -MI instead of outliers were examined on the artificial and a real data set. Furthermore, robust PCA based on minimum covariance determinant (MCD), PCA based on estimates obtained by EM instead of outliers and PCA based on estimates obtained by MI instead of outliers were compared with the results of CPCA. In this study, we tried to show the effects of using estimates obtained by MI and EM instead of outliers, depending on the ratio of outliers in data set. Finally, when the ratio of outliers exceeds 20%, we suggest the use of estimates obtained by MI and EM instead of outliers as an alternative approach.

Techniques for Robust Imputation in Incomplete Two-Way Tables

“…When data were incomplete (10% and 20% of missing values), but without contamination, the SVD88 algorithm always obtained the smallest prediction errors. This behavior is as expected, since without outliers the procedures based on least squares generally perform well [12]. This situation changes completely when there is contamination of the data with 5, 10 and 15% of outliers.…”

“…The presence of outliers in a data set can reduce the effectiveness of least squares techniques [12], which in this case is the standard SVD. To avoid this behavior, robust lower-rank approximations or equivalent robust SVD could be used.…”

“…A general method free of structural and distributional assumptions was originally proposed by Krzanowski [10] and recently generalized by Arciniegas-Alarcón et al [11] to complete matrices from multi-environmental experiments. The method depends on the SVD, which is a least squares technique, but a disadvantage of these types of techniques is that they are highly influenced by untypical values or outliers [12].…”

Aykırı Değer Varlığında Cox Regresyon Analizi için Yeni Bir Yaklaşım

“…Araştırmaların çoğunda aykırı değerler, modeldeki parametre tahminlerini etkileyebilir, seçilen modeli değiştirebilir ve modele dayanan tahminleri etkileyebilir düşüncesiyle veriden çıkarılarak, verilerin tekrar modellenmesi yoluna başvurmaktadır. Fakat bu da veri kümesinin küçülmesine ve aykırı değerin bulunduğu gözlemin sahip olduğu diğer önemli bilgiler içeren bağımsız değişken değerlerinin de silinmesine neden olmaktadır [1]. Bu yüzden bu çalışmada veri kümesinde bulunan aykırı değerli gözlemin tümünü silmek yerine sadece aykırı değeri silerek, yerine çoklu değer atama yöntemi ile değer atayarak aykırı değer probleminin çözülmesi amaçlanmaktadır.…”

Robust Principal Component Analysis based on Fuzzy Coded Data

“…Among other proposals for RPCA are the orthogonal PCA method developed by Maronna [3] and spherical PCA method developed by Locantore et al [4]. Alkan et al [5] examined if the missing value imputation methods can be used as an alternative approach to the RPCA. Alkan [6] also adapted minimum covariance determinant (MCD) method using the jacknife resampling approach and he examined the impacts of the changes resulting from this adaptation on RPCA based on MCD.…”